Question

A merchant surveyed 500 people to determine the way they learned about an upcoming sale. The survey showed that 290 learned about the sale from the​ radio, 250 from​ television, 250 from the​ newspaper, 140 from radio and​ television, 130 from radio and​ newspapers, 120 from television and​ newspapers, and 70 from all three sources. How many people learned of the sale from radio or television but not the​ newspaper?

Answer 1

There are 220 people learned of the sale from radio or television

but not the​ newspaper

Step-by-step explanation:

A merchant surveyed 500 people to determine the way they learned

about an upcoming sale

The survey showed that:

• 290 learned about the sale from the​ radio
• 250 from​ television
• 250 from the​ newspaper
• 140 from radio and​ television
• 130 from radio and​ newspapers
• 120 from television and​ newspapers
• 70 from all three sources

To solve this problem by an easy way draw a Venn-diagram represents

the survey

In the attached figure:

There are 3 intersected circles R for radio , T for television and N for

newspaper

Let us fill it by the given

∵ There are 70 learned from all three sources

∴ R ∩ T ∩ N = 70

∴ Write in the common part of R , T and N 70

∵ There are 140 from radio and​ television

- Subtract 70 from 140 to get R ∩ T only

∴ Write in the common part of R and T not in N 140 - 70 = 70

∵ There are 130 learned from radio and​ newspaper

- Subtract 70 from 130 to get R ∩ N only

∴ Write in the common part of R and N not in T 130 - 70 = 60

∵ There are 120 learned from television and​ newspaper

- Subtract 70 from 120 to get T ∩ N only

∴ Write in the common part of T and N not in R 120 - 70 = 50

∵ There are 290 learned about the sale from the​ radio

∴ There are 290 - 70 - 70 - 60 = 90 learned from the radio only

∵ There are 250 learned about the sale from the​ television

∴ There are 250 - 70 - 70 - 50 = 60 learned from the television only

∵ There are 250 learned about the sale from the​ newspaper

∴ There are 250 - 70 - 60 - 50 = 70 learned from the newspaper only

∵ There are 500 people in the survey

∵ There are 90 + 70 + 60 + 50 + 70 + 60 + 70 = 470 in R, T and N

∴ There are 500 - 470 = 30 not learned from the three sources

∴ Write 30 in the region outside the circles

∵ We need to find the people learned from radio or television but

   not the​ newspaper

- Add all the numbers in circles R and T but not in circle N

∵ 90 + 70 + 60 = 220

∴ There are 220 people learned of the sale from radio or television

   but not the​ newspaper

There are 220 people learned of the sale from radio or television

but not the​ newspaper

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